I used to think the same thing when I was only using a scrap as a "spider" (a starter piece that looks like a spider after all the threads are hanging off it). I would throw it away and think "what a waste, but at least the needle isn't eating the corners of my good fabric."
Then I discovered leaders in the form of 2.5" squares. I keep a small box of them near my machine. Two together act as my spider, and the needle then glides smoothly onto my "real" project. Two by two you're building a second quilt, wasting no thread or fabric. Make 4 patches, 9 P, 16P , 25, or a postage stamp quilt without adding extra time. I make doll quilt backs with mine.